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Ion-specific colloidal aggregation: population balance equations and potential of mean force

Recently reported colloidal aggregation data obtained for different monovalent salts (NaCl, NaNO$_3$, and NaSCN) and at high electrolyte concentrations are matched with the stochastic solutions of the master equation to obtain bond average lifetimes and bond formation probabilities. This was done for a cationic and an anionic system of similar particle size and absolute charge. Following the series Cl$^-$, NO$_3^-$, SCN$^-$, the parameters obtained from the fitting procedure to the kinetic data suggest: i) The existence of a potential of mean force (PMF) barrier and an increasing trend for it for both latices. ii) An increasing trend for the PMF at contact, for the cationic system, and a practically constant value for the anionic system. iii) A decreasing trend for the depth of the secondary minimum. This complex behavior is in general supported by Monte Carlo simulations, which are implemented to obtain the PMF of a pair of colloidal particles immersed in the corresponding electrolyte solution. All these findings contrast the Derjaguin, Landau, Verwey, and Overbeek theory predictions.